A340552 - OEIS

%I #5 Jan 19 2021 13:17:16

%S 1,0,8,8,3,3,6,9,3,5,2,6,8,3,4,2,0,5,2,6,7,3,5,7,7,5,0,5,9,5,7,0,2,5,

%T 0,6,9,9,8,1,3,4,0,8,6,6,9,6,2,1,7,5,2,8,4,3,5,4,2,8,0,2,1,6,2,8,4,5,

%U 0,4,9,7,5,1,5,0,2,7,0,7,2,8,2,7,5,5

%N Decimal expansion of Product_{primes p == 5, 7, 11 (mod 12)} 1/(1 - 1/p^2).

%H Salma Ettahri, Olivier Ramaré, and Léon Surel, <a href="https://arxiv.org/abs/1908.06808">Fast multi-precision computation of some Euler products</a>, arXiv:1908.06808 [math.NT], 2019.

%H Étienne Fouvry, Claude Levesque, and Michel Waldschmidt, <a href="http://arxiv.org/abs/1712.09019">Representation of integers by cyclotomic binary forms</a>, arXiv:1712.09019 [math.NT], 2017 and <a href="https://doi.org/10.4064/aa171012-24-12">Acta Arithmetica</a>, online 15 March 2018.

%F A340552^(1/2) = A301430 / (3^(1/4)*Pi^(1/2)*log(2+sqrt(3))^(1/4)/(2^(5/4)* Gamma(1/4))), see É. Fouvry et al.

%e 1.0883369352683420526735775059570250699813408669621752843542802162845...

%t (* Using Vaclav Kotesovec's function Z from A301430. *)

%t $MaxExtraPrecision = 1000; digits = 90;

%t digitize[c_] := RealDigits[Chop[N[c, digits]], 10, digits - 1][[1]];

%t digitize[Z[12, 5, 2] Z[12, 7, 2] Z[12, 11, 2]]

%Y A301430.

%K nonn,cons

%O 0,3

%A _Peter Luschny_, Jan 19 2021